pajczur
7th May 2017, 15:54
Hello,
I'm tryung to implement Fast Fourier Transformation. And I'm not sure if I understand it correctly.
As I understand when I transform (for example) simple sine wave by FFT, and than make inversion I should get exactly the same sine wave. Am I right?
But in some way it doesn't work for me. I found that code with the friend google:
#include <complex>
#include <iostream>
#include <valarray>
#include <QVector>
using namespace std;
const double PI = 3.141592653589793238460;
typedef std::complex<double> Complex;
typedef std::valarray<Complex> CArray;
// Cooley–Tukey FFT (in-place, divide-and-conquer)
// Higher memory requirements and redundancy although more intuitive
void fft(CArray& x)
{
const size_t N = x.size();
if (N <= 1) return;
// divide
CArray even = x[std::slice(0, N/2, 2)];
CArray odd = x[std::slice(1, N/2, 2)];
// conquer
fft(even);
fft(odd);
// combine
for (size_t k = 0; k < N/2; ++k)
{
Complex t = std::polar(1.0, -2 * PI * k / N) * odd[k];
x[k ] = even[k] + t;
x[k+N/2] = even[k] - t;
}
}
// inverse fft (in-place)
void ifft(CArray& x)
{
// conjugate the complex numbers
x = x.apply(std::conj);
// forward fft
fft( x );
// conjugate the complex numbers again
x = x.apply(std::conj);
// scale the numbers
x /= x.size();
}
int main()
{
const Complex test[] = { 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 };
CArray data(test, 8);
// forward fft
fft(data);
std::cout << "fft" << std::endl;
for (int i = 0; i < 10; ++i)
{
std::cout << data[i] << std::endl;
}
// inverse fft
ifft(data);
std::cout << std::endl << "ifft" << std::endl;
for (int i = 0; i < 10; ++i)
{
std::cout << data[i] << std::endl;
}
return 0;
}
So as I understand by ifft(data) I should receive the same as it was on the beggining, but the results are quite different. Can anyone help me?
For any help thanks in advance.
Best Regards
I'm tryung to implement Fast Fourier Transformation. And I'm not sure if I understand it correctly.
As I understand when I transform (for example) simple sine wave by FFT, and than make inversion I should get exactly the same sine wave. Am I right?
But in some way it doesn't work for me. I found that code with the friend google:
#include <complex>
#include <iostream>
#include <valarray>
#include <QVector>
using namespace std;
const double PI = 3.141592653589793238460;
typedef std::complex<double> Complex;
typedef std::valarray<Complex> CArray;
// Cooley–Tukey FFT (in-place, divide-and-conquer)
// Higher memory requirements and redundancy although more intuitive
void fft(CArray& x)
{
const size_t N = x.size();
if (N <= 1) return;
// divide
CArray even = x[std::slice(0, N/2, 2)];
CArray odd = x[std::slice(1, N/2, 2)];
// conquer
fft(even);
fft(odd);
// combine
for (size_t k = 0; k < N/2; ++k)
{
Complex t = std::polar(1.0, -2 * PI * k / N) * odd[k];
x[k ] = even[k] + t;
x[k+N/2] = even[k] - t;
}
}
// inverse fft (in-place)
void ifft(CArray& x)
{
// conjugate the complex numbers
x = x.apply(std::conj);
// forward fft
fft( x );
// conjugate the complex numbers again
x = x.apply(std::conj);
// scale the numbers
x /= x.size();
}
int main()
{
const Complex test[] = { 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0 };
CArray data(test, 8);
// forward fft
fft(data);
std::cout << "fft" << std::endl;
for (int i = 0; i < 10; ++i)
{
std::cout << data[i] << std::endl;
}
// inverse fft
ifft(data);
std::cout << std::endl << "ifft" << std::endl;
for (int i = 0; i < 10; ++i)
{
std::cout << data[i] << std::endl;
}
return 0;
}
So as I understand by ifft(data) I should receive the same as it was on the beggining, but the results are quite different. Can anyone help me?
For any help thanks in advance.
Best Regards